Problem of the Week 1187

Find the Head-Averse Coin

We have two coins: coin A gives heads with probability 1/3; coin B gives heads with probability 9/10.

One of the two, call it C, is selected randomly (using equal probability).

Devise a scheme that involves flipping C at most n times, looking at the results, and declaring whether C = A or C = B. We want the declaration to be correct at least 999,999 times out of a million. And we want n to be as small as possible.

Source: Suggested by Michael Elgersma

Aside: One could imagine a different method of gathering evidence, where one flips one of them m times and the other n times, trying to minimize the total number of flips. I have not thought about that.